Current passing through a conductor generates heat due to I2R power dissipation. The current-carrying capacity of a conductor is the maximum current which can be carried continuously, under specified conditions, without causing objectionable degradation of the insulating or electrical properties. At the rated, current-carrying capacity, the heat is dissipated harmlessly from the conductor to the environment. The temperature in a conductor, such as those on a printed wiring board or in a wire harness, rises due to I2R heating. Above the current-carrying capacity the I2R heat can exceed the temperature rating of the insulation. For a wire with a known resistance, the temperature rise is proportional to the integral of I2 with respect to t, ∫I2dt.
Manufacturers of wire harnesses and airframe manufacturers specify the maximum allowable value of this integral so that any current overload in the wire harness will be limited. An I2t Trip Time vs. Percent Current-Carrying Capacity curve has been published in Mil Standard 1760. A major airframe manufacturer also has published an I2t Trip Time vs. Percent Current-Carrying Capacity curve suitable for their aircraft applications. This plot has been widely copied, and is a de facto industry standard. FIG. 1 is a typical representation of this I2t Trip Time vs. Percent Current-Carrying Capacity. These I2T curves are essentially constant energy plots, i.e., plots of the maximum allowable energy, on axes of time and current squared, where the resistance has been normalized to one.
Mechanical circuit breakers have been used to protect wires from overheating by abnormally high currents. Turning on a circuit breaker into a capacitive load results in high in-rush currents that may be more than 10 times the rated current-carrying capacity. Conversely turning off highly inductive loads results in a large voltage, or inductive kick, which may exceed, the voltage rating of the wire insulation. Contact erosion, caused by arcing in these load types, limits circuit breaker life and produces severe EMI (electromagnetic interference) problems.
Since mechanical circuit breakers do not lend themselves well to computer control, solid state power controllers, SSPCs, are used. SSPCs eliminate contact arcing, reduce the peak in-rush current into capacitive loads and reduce the EMI. All circuit breakers have a rated current capacity and an associated “trip time”, which is the time to “trip” or break the circuit at a specified overload condition. SSPCs more accurately monitor the power density in the conductor, allowing tighter control of the trip time.
In analog control of an SSPC, the square of the load current is integrated in an operational amplifier. The output of the operational amplifier (i.e., the energy) is applied to a comparator. The reference of the comparator represents the maximum allowable energy that may be applied to the load (e.g. a wire). When the maximum energy supplied exceeds this reference, the load is disconnected from the line. This analog circuitry is complex and prone to inaccuracy. This is especially true when the circuits are operating at a slight overload above their rated, current-carrying capacity. It is common practice to accommodate these errors by derating the current-carrying capacity.
McCollum et al., U.S. Pat. No. 4,445,183 describe a control means wherein an alternating current is sampled in intervals dictated by the frequency of the current. A squared digital current amplitude signal, corresponding to the sample, is added to an accumulator and a first predetermined constant is subtracted from the accumulator after each addition of the sampled squared digital current amplitude signal. The value in the accumulator is compared with a second predetermined constant, and the control means provides a trip signal in response to an accumulator value exceeding the second predetermined constant. Fifty and sixty hertz currents are sampled every 20 milliseconds and 16.7 milliseconds respectively. With the low sampling frequencies employed, the value in accumulator does not adequately represent the overload energy applied. Aircraft often use 400 hertz power, which would be sampled every 2.5 milliseconds. However, frequency control in aircraft is not accurate. Furthermore, the newer “dirty power” in aircraft runs directly off the engine and the frequency varies from well below 400 hertz up to as high as 800 hertz. With poor frequency control or “dirty power”, in order determine the overload energy supplied it is necessary to measure the time interval between current samples and multiply the square of each current sample measurement by the appropriate time interval. In many applications current sampling intervals less than 1 millisecond are needed to accurately measure the overload currents.
Tripodi in U.S. Pat. No. 5,195,012 also discusses the use of sum of the square of the overload current to activate a trip signal. Tripodi introduces a second control function used after the sum of the squares of the overload current reaches a fixed value. This function is the sum of the squares of total current, and the trip signal is sent after this function reaches a predetermined maximum. To overcome problems associated with frequency variation Tripodi samples the current 4, 8 or 16 times, and averages the samples, the averaged samples thus represent time periods of 10, 20 or 40 milliseconds respectively.
The SSPC must not only protect the wire, but it must also protect its switching elements. When solid state switching elements are required to turn on into highly reactive loads, current limiting or foldback current limiting is used. In order to turn on in these modes, the power dissipated in the switching elements should be monitored. The manufacturers of solid state switching elements specify the maximum energy dissipation. To keep the device within this “safe operating area” (SOA) it is necessary to monitor the voltage across the switching element; multiply it by the current, and integrate the I·E product with respect to time, ∫(I·E)dt. The analog multiplying and integrating circuits used to measure this are complex. As a result the calculation is relatively inaccurate and will drift with temperature. This requires the “safe operating area” to be significantly “guard banded” or derated.